Comments

Why not make a game with 2 separated boards.
One player is white on one board and the other is white on the other board. With that no player will have first-move advantage.
Of course one rule to see who will win need to be decided. If the first one that mate the enemy (on any of the boards) win, being fast at mating would be more important than just mating, this is a not wanted thing.
Maybe do like that. If one guy win on both boards, he win the game. He both players win on one board, they play again.

Maybe, make variant, wich uses sets of diffirent games? For example, 9x23
board, pieces from European, Chinese and Japanese chess: European pawns
have duble step, Chinese pawns gets sideways moves on 5th rank, Chinese
elephants may go to 5th rank, but not further.
Maybe using games with different number of ranks is not good, better to use
games of same number of ranks, for example, European, Thai and Mongolian
chess or Chines and Korean chess or Japanese and Cambodian.

On 8x16 there are 19 bounces possible at most, overlaying the Billiards Mutator for Bishop and Queen. Place Bishop at c2 for convenience and assume no obstruction. c2-b1-Bounce to a2-Bounce to b3-c4-d5-e6-f7-g8-Bounce to h7-i6-j5-k4-l3-m2-n1-Bounce to o2-p3-Bounce to o4-n5-m6-l7-k8-Bounce to j7-i6-h5-g4-f3-e2-d1-Bounce to c2-b3-a4-Bounce to b5-c6-d7-e8-Bounce to f7-g6-h5-i4-j3-k2-l1-Bounce to m2-n3-o4-p5-Bounce to o6-n7-m8-Bounce to l7-k6-j5-i4-h2-g2-f1-Bounce to e2-d3-c4-b5-a6-Bounce to b7-c8-Bounce to d7-e6-f5-g4-h3-i2-j1-Bounce to k2-l3-m4-n5-o6-p7-Bounce to o8-Bounce to n7-m6-l5-k4-j3-i2-h1-Bounce to g2-f3-e4-d5-c6-b7-a8. It means a Bishop on c2 can reach a8 in one move, but not very directly. Billiards 'Bishop c2-Bishop-a8' requires the above 19 bounces. Whereas, Elbow Bishop 'c2-a8' is accomplished c2-d3-e4-(90 degrees)d5-c6-b7-a8 in the one change of direction, a pretty direct route. In sum, 6x8 has 7 bounces, 8x8 4 bounces, 8x10 7 bounces, 8x12 13 bounces, 8x14 15 bounces, 8x16 19 bounces. What is the formulaic pattern? '8x14' requires starting at g2 for best result (Hey, Geometria). There the bounces occur successively after g2 starting square at f1, a6, c8, j1, n5, k8, d1, a4, e8, l1, n3, i8, b1, a2, g8, and not possible anymore at arrival square n1. If the Bishop starts on m8 in 8x14, the number of squares actually traversed in that full route, extended back to m8 for maximization, is 77. Shorthand for this size 8x14 might be 'Bishop m8-n1(77 times one-stepping)'.

Another obvious extension is to have a second join at the other Rook files to give a wraparound variant. This would give an extra symmetry in that any two pieces of the same traditional location (e.g. both Queen Knights, both King Rook Pawns) would be affected in exactly the same way. Has anyone ever done such a variant?